Gamow shell model and realistic nucleon-nucleon interactions

We present a new and efficient method to obtain a Gamow shell-model basis and matrix elements generated by realistic nucleon-nucleon interactions. We derive a self-consistent Hartree-Fock potential from the renormalized N³LO interaction model. The corresponding Gamow one-body eigenstates are generated in a plane wave basis in order to build a Gamow shell-model set of basis states for the closed shell nuclei ⁴He and ¹⁶O. We address also the problem of representing a realistic nucleon-nucleon interaction in a two-particle Berggren basis in the laboratory frame. To achieve this, an expansion of matrix elements of the residual nucleon-nucleon interaction in a finite set of harmonic oscillator wave functions is used. We show that all loosely bound and narrow resonant states converge surprisingly fast. Even broad resonances in these two-particle valence systems converge within a reasonable number of harmonic oscillator functions. Examples of ⁶He and ¹⁸O Gamow shell-model calculations using ⁴He and ¹⁶O as closed shell cores are presented. This procedure allows Gamow shell-model calculations to be performed with all realistic nucleon-nucleon interactions and with either momentum or position space representations for the Gamow basis. Perspectives for nuclear structure calculations of dripline nuclei are outlined.